A quadrant has an area of 175m2. Find the length of its base
To find the length of the base of a quadrant given the area, we need to follow these steps:
Step 1: Understand the problem
A quadrant is one-fourth of a circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. However, we need to find the length of the base, which is only a part of the circle.
Step 2: Determine the radius of the quadrant
Since the area is given, we can use the formula for the area of a circle to find the radius. Rearranging the formula, we have r = √(A/π).
Given that the area is 175m^2, we can calculate the radius:
r = √(175/π).
Step 3: Calculate the length of the base
The length of the base of the quadrant is the same as the circumference of a quarter of a circle. The formula for the circumference of a circle is C = 2πr, and for the quarter of a circle, it would be C/4.
So, the length of the base would be C/4 = (2πr)/4 = (πr)/2.
Substituting the value of r from step 2, we get:
length of the base = (πr)/2 = π√(175/π)/2.
Simplifying this expression:
length of the base = (√175π)/2.
Therefore, the length of the base of the quadrant is (√175π)/2 meters.